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If X follows a binomial distribution with parameters n = 100 and p = 1/3, then P (X = r) is

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A biased coin with probability p, 0 < p < 1, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is 2/5, then p equals.

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If X follows a binomial distribution with parameters n = 8 and p = 1/2, then P (|X – 4)| ≤ 2) equals.

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A fair die is tossed eight times. The probability that a third six is observed in the eight throw is

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Fifteen coupons are numbered 1 to 15. Seven coupons are selected at random, one at a time with replacement. The probability that the largest umber appearing on a selected coupon is 9, is